Raymond Hettinger <raymond.hettin...@gmail.com> added the comment:

Here are a few other data points.  There is no consensus but either returning 0 
or erroring out seem reasonable.

MS Excel's COMBIN: If number < 0, number_chosen < 0, or number < number_chosen, 
COMBIN returns the #NUM! error value.

Scipy.misc.comb: If k > N, N < 0, or k < 0, then a 0 is returned.

Matlib.nchoose: Error: K must an integer between 0 and N.

Maple.numbcomb: Unclear from the docs what this does

Wolfram alpha:  Returns 0
https://www.wolframalpha.com/input/?i=10+choose+12

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